{"paper":{"title":"An extension of the Beckner's type Poincar\\'e inequality to convolution measures on abstract Wiener spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Lanconelli, Aurel I. Stan, Paolo Da Pelo","submitted_at":"2014-09-20T06:31:56Z","abstract_excerpt":"We generalize the Beckner's type Poincar\\'e inequality \\cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\\mu\\star\\nu$, where $\\mu$ is the reference Gaussian measure and $\\nu$ is a probability measure satisfying a certain integrability condition. As the Beckner inequality interpolates between the Poincar\\'e and logarithmic Sobolev inequalities, we utilize a family of products for functions which interpolates between the usual point-wise multiplication and the Wick product. Our approach is based on the positivity of a quadratic form involving Wick p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5861","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}